MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex2_1_3

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-15. p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-15.00000001 (ANTIGONE) -15.00000001 (BARON) -15. (COUENNE) -15. (CPLEX) -15. (GUROBI) -15. (LINDO) -15. (SCIP)
Referencesⓘ	Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999.
Sourceⓘ	Test Problem ex2.1.3 of Chapter 2 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QP
#Variablesⓘ	13
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	concave
#Nonzeros in Objectiveⓘ	13
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	9
#Linear Constraintsⓘ	9
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	27
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	4
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	4
#Blocks in Hessian of Lagrangianⓘ	4
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	1.0000e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         10        1        0        9        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         14       14        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         41       37        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10;


e1.. -(5*x1 - 0.5*(10*x1*x1 + 10*x2*x2 + 10*x3*x3 + 10*x4*x4) + 5*x2 + 5*x3 + 5
     *x4) + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 + x13 + objvar =E= 0;

e2..    2*x1 + 2*x2 + x10 + x11 =L= 10;

e3..    2*x1 + 2*x3 + x10 + x12 =L= 10;

e4..    2*x2 + 2*x3 + x11 + x12 =L= 10;

e5..  - 8*x1 + x10 =L= 0;

e6..  - 8*x2 + x11 =L= 0;

e7..  - 8*x3 + x12 =L= 0;

e8..  - 2*x4 - x5 + x10 =L= 0;

e9..  - 2*x6 - x7 + x11 =L= 0;

e10..  - 2*x8 - x9 + x12 =L= 0;

* set non-default bounds
x1.up = 1;
x2.up = 1;
x3.up = 1;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.up = 1;
x8.up = 1;
x9.up = 1;
x13.up = 1;

* set non-default levels
x1.l = 1;
x2.l = 1;
x3.l = 1;
x4.l = 1;
x5.l = 1;
x6.l = 1;
x7.l = 1;
x8.l = 1;
x9.l = 1;
x10.l = 3;
x11.l = 3;
x12.l = 3;
x13.l = 1;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;